Hvac control system and method

ABSTRACT

A method of controlling the heating, ventilation and air conditioning (HVAC) system of a building, the method comprising the steps of: (a) developing an initial thermal model of the building, and continuously updating the thermal model over time; (b) utilising the thermal model to continuously develop a daily HVAC operating plan for the building; and (c) continuously examining a current HVAC operating plan and optimising the alignment of the current HVAC operation with the current HVAC operating plan.

FIELD OF THE INVENTION

The present invention relates to an efficient system and method forHeating, Ventilating and Air conditioning (HVAC) of a building. Inparticular, the present invention provides to a more efficient climatecontrol system for use in buildings.

BACKGROUND

The widespread deployment of heating, ventilation and air-conditioning(HVAC) systems has added significant flexibility to building design andform. It has provided indoor comfort even in severe climatic conditionsand served to make habitable buildings with poor thermal performance.This flexibility has not, however, been without its costs. For example,in Australia, HVAC typically accounts for over 60% of energy use incommercial buildings [Australian Greenhouse Office, 1999], and is asubstantial contributor to greenhouse gas emissions and is drivingdemand in the electricity network.

There is considerable research being carried out into optimal HVACcontrol strategies. These have considered aspects of comfort,electricity network interactions, and greenhouse gas emissions, thoughtypically in isolation. For example, Braun et al. (1990, 2001) hasinvestigated using building thermal mass for energy load shaping, Eto(2007) has demonstrated the use of air-conditioning to provide spinningreserve to the electricity network, Fanger (19617) pioneered research onthermal comfort, and the effects of thermal comfort on productivity havemore recently been investigated by Seppänen et al. (2006). Greenhousegas emissions have typically been achieved as part of overall energysavings strategies, though cogeneration systems (e.g. White and Ward(2006)) have directly exploited waste heat and fuel substitution toreduce emissions.

HVAC control systems typically use temperature as their control setpointthroughout a commercial building. The HVAC plant, including valve anddamper positions, fan speeds, and so on are controlled in order toachieve a given setpoint temperature. Typically, this setpointtemperature is fixed, although state of the art HVAC systems may varytemperature based on a load shedding request.

SUMMARY

It is an object of the present invention to provide an improved form ofHVAC control system having a number of desirable features.

In accordance with a first aspect of the present invention, there isprovided a method of controlling the heating, ventilation and airconditioning (HVAC) system of a building, the method comprising thesteps of: (a) developing an initial thermal model of the building, andcontinuously updating this thermal model over time; (b) utilising thethermal model to continuously develop a daily HVAC operating plan forthe building; and (c) continuously examining the current HVAC operatingplan and optimising the alignment of the current HVAC operation withthis plan.

The thermal model utilises a series of parameters, fitted to historicalthermal data for the building. The thermal model can be a piecewisepolynomial model. The initial thermal model can be iteratively updatedsubstantially daily. The daily operating plan is an optimisation of acombination of operator preferences that includes user comfort, powerconsumption and power costs. External inputs beyond operator preferencesthat drive the operating plan include electricity pricing data, weatherforecasts and occupant comfort satisfaction data. The daily HVACoperating plan can be recalculated substantially every 5 minutes.Optimising the alignment of HVAC operation with the current HVACoperating plan can be attempted substantially every 10 seconds.

In accordance with a further aspect of the present invention, there isprovided a method of controlling the heating, ventilation and airconditioning (HVAC) system of a building, the method comprising thesteps of: (a) determining a thermal model for the building; (b)determining an expected human comfort model for users of the building;(c) utilising the expected human comfort model as the prime factor incalculating a HVAC operating plan of the building.

The human comfort model can be augmented with personal comfort data ofusers of the commercial building by means of data feed back by users ofthe commercial building. The human comfort model can be derived from theASHRAE standard comfort models.

The thermal model in one embodiment has the following form:

${T_{int}(z)} = {{{F_{amb}(z)}{T_{amb}(z)}} - {\frac{10}{P_{coolTyp}}{F_{Pcool}(z)}{P_{cool}(z)}} + {\frac{1}{P_{heatTyp}}{F_{Pheat}(z)}{P_{heat}(z)}} + {B(z)}}$

where: T_(int)(z) is the average internal building temperature;T_(amb)(z) is the ambient temperature; P_(cool)(z) is the HVAC coolingpower consumption;

P_(coolTyp) is the typical HVAC cooling power consumption; it is used in(1) as a scaling factor to get the magnitude of the parameters ofF_(Pcool)(z) in the same ball park as other parameters; also it providesa normalization mechanism that allows for operation on different BMSsystems—this is particularly important with respect to optimizationconstraints

P_(heat)(z) is the HVAC heating power consumption

P_(heatTyp) is the typical HVAC heating power consumption; it is used in(1) as a scaling factor to get the magnitude of the parameters ofF_(Pheat)(z) in the same ball park as other parameters; also it providesa normalization mechanism that allows for operation on different BMSsystems—this is particularly important with respect to optimizationconstraints

F_(amb)(z) captures the internal building temperature response toambient temperature

F_(Pcool)(z) captures the internal building temperature response to HVACcooling power

F_(Pheat)(z) captures the internal building temperature response to HVACheating power

B(z), “baseline”, captures factors other than those captured byF_(amb)(z), F_(Pcool)(z) and F_(Pheat)(z)

10 is a scaling factor used to get the magnitude of the parameters ofF_(Pcool)(z) in the same ball park as other parameters; this number wasan arbitrary choice.

In other embodiments, the thermal model can have substantially thefollowing form:

T _(z) =F _(A)(s)·T _(Amb)+BaselineFcn−F _(T)(s)·ΔT _(SS)

where: T _(z) is (modelled) aggregate zone temperature; T_(Amb) is theoutside (Ambient) air temperature; ΔT_(SS) is the steady statedifference in zone temperature that would result from the current HVACcooling and heating powers; BaselineFcn is a learnt function of time,accounting for people, equipment, sun, etc; F_(A)(s) and F_(T)(s) arelinear time invariant filters, accounting for the system dynamics.

Ideally ΔT_(SS) has the form:

ΔT _(SS)=α_(c)·μ_(c)·max{0,P _(Cool) −P _(cb)}−α_(h)·μ_(h)·max{0,P_(Heat) −P _(hb)}

where the first part of the equation is the effective coolingtemperature (ΔT_(Cool)), the second part is the effective heatingtemperature (ΔT_(Heat)), and the parameters are: P_(Cool) and P_(Heat)are estimates of actual cooling and heating powers respectively (kW);P_(cb) and P_(hb) are baseline cooling and heating powers respectively(kW); α_(c) and α_(h) are nominal scaling for HVAC power effectiveness(° C./kW); and μ_(c) and μ_(h) are HVAC efficiency de-ratings as afunction of external temperature.

In the above preferred form, the baseline function preferably changesdepending on the current day of the week. More preferably, the baselinefunction is formed of a combination of triangular basis functions thatare estimated at specific fixed points throughout a day.

BRIEF DESCRIPTION OF THE DRAWINGS

Benefits and advantages of the present invention will become apparent tothose skilled in the art to which this invention relates from thesubsequent description of exemplary embodiments and the appended claims,taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a schematic illustration of the operational environment of aHVAC system;

FIG. 2 illustrates a schematic block diagram of the Opticool System ofthe preferred embodiment;

FIG. 3 illustrates schematically the functionality of the commercialbuilding model development;

FIG. 4 illustrates schematically the comfort based zone control;

FIG. 5 illustrates an example interface for thermal comfort modelling ofa zone;

FIG. 6 illustrates the thermal modelling loop for modelling the thermalbehaviour of a commercial building;

FIG. 7 illustrates a commercial building power planning loop;

FIG. 8 illustrates the temperature control loop;

FIG. 9 illustrates the results of modelling commercial building zonetemperatures.

FIG. 10 illustrates a set of triangular basis functions used to create abaseline function for a building model of one embodiment of theinvention;

FIG. 11 illustrates a full set of 12 triangular basis functions used tocreate a baseline function for a full day of a building model;

FIG. 12 illustrates an example of the relationship between heating andcooling power parameters;

FIG. 13 illustrates the process of merging actual measured temperatureswith forecast ambient temperatures;

FIG. 14 illustrates different fuel use by type for Australian CommercialBuildings; and

FIG. 15 illustrates an example graphical user interface for fuel pricespecification.

DETAILED DESCRIPTION

Preferred embodiments of the invention will now be described, by way ofexample only, with reference to the accompanying drawings.

In the preferred embodiment there is provided a control system whereinthe fundamental setpoint for the system is not temperature but humancomfort (a “predicted mean vote” measure). In the preferred embodiments,a human comfort goal is first established, and from this goal zonetemperatures, and then plant parameters such as valve and damperpositions, fan speeds and so on are controlled in order to achieve thiscomfort setpoint. This is to be contrasted with the prior art whichnormally rely on temperature based setpoint schemes. For example, therecould be a range of different temperatures that all achieve the samecomfort setpoint. Performance wise, by using human comfort as thefundamental control parameter, it is possible to realise significantenergy and cost savings, whilst maintaining a particular level of humancomfort.

The system of the preferred embodiment also provides a system and methodthat continuously updates the thermal model of the commercial building.The preferred embodiment relies upon a continuously adjustable thermalmodel of the commercial building. In the preferred embodiment, thecontrol system continuously re-learns thermal and comfort models, andsubsequently re-plans the behaviour of the commercial building at veryregular intervals. In one example embodiment, the following plannedsteps are taken:

Once a day, the system uses historical performance data to learn athermal model of the commercial building. This model includes specificconsideration of the time of day and day of the week, so the generatedthermal model is cognisant of time of day and day of the week.

Every 5 minutes the system creates a new plan for the day ahead's HVACoperation. By regularly updating the day-ahead operating plan, thesystem is able to adapt to changing weather and commercial buildingusage patterns throughout the day.

Every 10 seconds the system examines the day-ahead operating plan,compares its current state to the planned state, and controls the HVACplant to strive towards adhering to the day-ahead operating plan.

The continuous learning and re-planning behaviour provides a performanceadvantage in that the system is able to cope with dynamic changes to thecommercial building—both fast (for example, a sudden influx of occupantschanging the thermal response of a section of the commercial building)or slow (for example, trees growing up alongside the western wall of abuilding, changing its thermal response late in the afternoon). Further,in practice, Commercial Buildings and HVAC systems often move away fromthe state they were in at initial commissioning, and without continuouslearning and adaptation, the subsequent poor performance of the HVACsystem can result in poor human comfort and low energy efficiency.

HVAC control in a typical commercial building is carried out by abuilding management system—a computer program and related hardware,actuators, sensors and controllers that measures and adjusts chiller,heater and air handling unit operation to regulate temperature for thecommercial building occupants.

To improve commercial building energy performance, a more advancedapproach is required, that manages resources such as energy consumptionand financial expenditure, whilst providing appropriate environmentalconditions. Having considered the various types of resources and desiredenvironmental conditions, the role of an advanced commercial buildingcontrol system is to allow a balance to be found between what areinevitably competing goals. Finding a suitable balance is one of the keyfunctions of the preferred embodiment.

Features of the HVAC control system of the preferred embodiment that arenot included in common HVAC controllers include:

-   -   An awareness of different energy sources and the implications of        their usage—for example a commercial building may use natural        gas based heating, and electricity based cooling. Different fuel        types have different cost and greenhouse gas implications, while        the particular plant items which are utilised at different load        levels operate with different efficiencies.    -   Use of forecasting to move away from a reactionary control        philosophy. As an example, many commercial buildings in        temperate climates will operate in heating mode in the morning,        followed by cooling mode later in the day. By taking into        account anticipated weather and thermal loads later in the day,        heating can be appropriately limited, thereby reducing both        heating load and the subsequent cooling load.    -   Explicit consideration of human comfort via thermal comfort        models and using measured temperatures and humidity and nominal        values of other factors (airspeed, clothing and activity        levels).    -   Further consideration of individual buildings and occupants.        Despite advances in thermal comfort research, the best measure        of comfort and satisfaction will always be feedback from the        building occupants themselves. The preferred embodiment includes        a mechanism for obtaining occupant feedback regarding thermal        comfort and satisfaction. This user feedback is used to        calculate a comfort offset map for each HVAC zone, which is        added to the computational thermal comfort model to reflect        local user preferences. Responding to actual user comfort        information at zone level provides the opportunity to drop below        the theoretical 5% lower bound on the percentage of people        dissatisfied in a building.    -   A mechanism for balancing (i) running costs, (ii) greenhouse gas        emissions and (iii) occupant thermal comfort when controlling        the HVAC system.

Implementation Details

Turning initially to FIG. 1, there is illustrated schematically, theoperational environment 1 of the preferred embodiment. The preferredembodiment, hereinafter referred to as the OptiCOOL control system 2, isa supervisory control system. That is, OptiCOOL interfaces, or is acomponent of, an existing building management system (BMS) 3, andprovides high-level commands to the BMS. The OptiCOOL control systemdoes not consider control of individual valves, fan speeds, interface tosensing or control equipment 4—these low level functions are left forthe BMS system 3. OptiCOOL interfaces 5 to the BMS through an HVACindustry standard communications interface (a number of these areavailable), and takes basic data from the BMS such as zone temperatures,chiller and fan set points. OptiCOOL 3 combines this HVAC plant datawith outside data 6 including electricity price, weather forecasts, usercomfort data and the thermal model for the building to make a controldecision that provides a basic zone setpoint temperature back to the BMS3. The BMS then manages the HVAC plant to achieve this setpointtemperature.

As noted previously, the OptiCOOL control system 3 is based aroundestablishing a day-ahead, or similar time period, operating plan for thewhole-building HVAC plant. The OptiCOOL control system is illustrated inmore detail in FIG. 2. To achieve such a plan 10, a thermal model of howthe building responds to weather and HVAC plant actions is needed. Themodel 11 is “learnt” from historical building data.

To enable intelligent scheduling of HVAC systems, a model is requiredthat can evaluate the system response to the range of possible controlactions. Once a model has been fitted to the system under control, it isable to be used as part of an optimisation loop which evaluates a rangeof possible control actions to identify an appropriate control strategy.FIG. 3 illustrates the basic HVAC model implicitly encapsulatingbuilding thermal performance, HVAC system behaviour and building thermalloads. Using external thermal conditions and zone power consumption asinputs, the model is able to learn their relationship to zoneconditions.

To identify a zone's response to setpoint changes and externalconditions, several modelling approaches could be utilised. In someembodiments, sophisticated learning techniques are employed. In otherembodiments a simple “black box” model is derived solely fromobservation of input/output characteristics, without explicit knowledgeof the underlying physical process being modelled. These latter modelsare particularly useful for complex and nonlinear multi-variablesystems, and the approach avoids the need for any manual configurationof system parameters. It was found that a simple polynomial approach wassuitable. The benefit of this model is that it is linear in the fittedparameters, substantially simplifying the model fitting process.

In one embodiment, a sophisticated learning process is implemented intothe HVAC model. This process involves the estimation of parameters ofthe model that aims to capture how the building responds to ambienttemperature, as well as HVAC cooling and heating power. An example ofsuch a model is described below under the section “Example of a BuildingModel”.

Input data can be manually entered, or appropriate interfaces to eachinformation source undertaken. For example, in one embodiment, Javainterfaces have been developed to obtain weather prediction data fromthe Australian Bureau of Meteorology, real time electricity pricinginformation from the Australian Electricity Market Operator, andbuilding occupant comfort survey results.

The polynomial model utilises HVAC power, ambient temperature and anidentified thermal baseload profile for the building to estimate theaverage zone temperature for the building. This model is based on theform:

$T_{Av} = {{\frac{{k_{1}s^{2}} + {k_{2}s} + k_{3}}{\left( {{\tau_{1}s} + 1} \right)\left( {{\tau_{2}s} + 1} \right)}T_{ambient}} + {\frac{{k_{4}s} + k_{5}}{\left( {{\tau_{1}s} + 1} \right)\left( {{\tau_{2}s} + 1} \right)}P_{HVAC}} + \begin{Bmatrix}{Initial} \\{Conditions}\end{Bmatrix} + \begin{Bmatrix}{Thermal} \\{Baseload}\end{Bmatrix}}$

Where T_(AV) is the is the average zone temperature throughout thebuilding, T_(ambient) is the ambient outside temperature, P_(HVAC) isthe total power consumed by the HVAC system, k1, k2, k3, k4, k5 areadjustable parameters obtained by best fit to measured data, τ₁, τ₁ arethe dominant thermal time constants of the building HVAC system, s isthe complex Laplace variable, ‘Initial Conditions’ accounts foruncertainty in the internal thermal states of the building fabric andHVAC system at the start of the measurement period. These initialconditions result in a transient that is a combination of the naturalmodes of the system and hence is of the form: k₆e^(−t/Σ1)+k₇e^(−t/τ2).These modes are explicitly identified so as to not bias the systemidentification. Thermal Baseload is an identified baseload profile thataccounts for different thermal loads throughout the day. This isdependant on factors such as solar gain and the activities of thebuilding occupants. The thermal baseload can be parameterised as apiecewise linear function. This baseload function is defined to beidentical for each day in the data set and is determined to beindependent of ambient temperature and HVAC power.

Utilising data from a trial building with a conventional VAV system,five minute interval data for 16 days was fitted to the polynomial modelusing regression analysis to determine the various parameters. Thecoefficient of determination of the fit over this data set is r₂=0.956,suggesting that the model provides a good fit. Additional second orderterms were evaluated (i.e. power squared) but they did not significantlyincrease the explained variance and so this was not included in themodel. An example of the resultant fit is shown in FIG. 9.

Once a building thermal model 11 has been established, this model isused together with a weather forecast and electricity tariff information6 to put together a consumption plan output 12 for the HVAC plant. Thisplan is a time series power profile for the building, based onaccumulating the power consumption of individual HVAC plant needed toachieve a predicted mean vote (PMV) comfort setpoint for the wholebuilding. To find and output this plan 12, an optimisation routineconsiders a large variety of possible power profiles for the building,and decides which profile to use based on a cost function that considersthe priority of occupant comfort, running expenditure and CO₂ emissions.Once the optimal (cost minimal in terms of the cost function) powerprofile 12 has been determined, this profile is then translated to awhole-building comfort profile, where a whole-building comfort setpointis determined for regular intervals throughout the day.

Once a whole-building comfort setpoint 15 is determined, actual HVACcontrol is based on separately controlling individual zones of thebuilding via zone control determination 16.

As shown in FIG. 4, (a screenshot from the control system), zone controlis based on three main function blocks: A comfort feedback block 41 thattakes user feedback based on a ComfortSENSE client application, andconverts this to a “percentage of people dissatisfied” figure. A zonecomfort model block 42, that takes zone temperature (provided by the BMSvia the OptiCOOL-BMS data link), and uses the ASHRAE-55 standard“Thermal Environmental Conditions for Human Occupancy” to calculatepredicted mean vote (PMV) 44 and predicted percentage of peopledissatisfied (PPD) figures for the zone. The functionality of this blockis shown in FIG. 5. The theoretical PMV and PPD figures are then offset45 by a measured PPD figure obtained from the comfort feedback block. Ifno data is available from the comfort feedback block (its usage isoptional), then the system will base its PMV/PPD figures entirely on thetheoretical ones calculated from the ASHRAE standard.

The zone control block 47 takes a predetermined comfort setpoint (PMV)for the zone from the whole-building control loop, zone and externaltemperature (from the BMS), and the actual PMV/PPD value from thecomfort model, and determines a zone setpoint temperature 48 to achievethe desired zone PMV setpoint.

Returning to FIG. 2, there are three core control loops in the OptiCOOLsoftware system 2: These include: A thermal modeling loop fordetermining the building thermal model 11, a power planning loop fordetermining a power consumption plan 10, and the building setpointdetermination loop for setting building zone setpoints. The threeforward-looking plans that the OptiCOOL software system creates arecontinuously optimised and updated. That is, building thermal models,feedback-adjusted human comfort models, and subsequently the wholebuilding power profile are updated at regular (predefined) controlintervals. This behaviour is significant, as it allows the system torespond to changing external factors such as sudden shifts in predictedelectricity price or weather forecast, building usage or human comfort.This behaviour results in an always-updating look-ahead profile of HVACpower consumption, human comfort and time. The three main loops canoperate as follows:

The Modeling Loop (FIG. 6)

A modelling loop, which executes once a day and forms the thermal model11 of the building that predicts internal temperature based on the dayof the week, time of day, HVAC power consumption and external weather.The steps in the loop include: loading historical power andcorresponding temperature profiles 61, calculating expected resultantpower and weather dependant factors 61, calculating constants for timeand day of the week factors 63 and assembling a polynomial model thatpredicts building temperature at a given day of the week, time, expectedexternal weather and HVAC power.

Power Planning Loop (FIG. 7)

The power planning loop, executes every 5 minutes, and creates a 24-hourahead planned HVAC power consumption profile 12 for the building. Thisloop first determines the current total HVAC power consumption,determines a future weather forecast and produces a minimal cost powerplan through optimization.

Setpoint Determination Control Loop (FIG. 8)

A whole building setpoint determination control loop 14, executes every10 seconds, taking the building power plan, and providing the BMS with azone setpoint temperature targeted at achieving this power plan. Thecontrol system uses human comfort as the planned parameter for everyHVAC zone of the building. Human comfort is translated in to physicalparameters such as indoor temperature and humidity by applying theASHRAE comfort models, including any shift based on local user feedback.Building parameters such as fan speed or valve set-points are notspecified as these are left to implementation by the incumbent BMS toascertain based on the zone temperature data provided.

The implemented system uses one modelling technique—the linear timeinvariant technique. This technique is based on using a constrainedleast squares fit algorithm to parameterise a third-order linear timeinvariant model of the building's thermal response.

Initial conditions for the system are established by operating thealgorithm on historical building performance data.

The intelligent HVAC supervisory control system can be readilyretrofitted to existing building management systems (BMS) throughindustry standard process control interfaces such as OPC. Theintelligent HVAC controller utilises machine learning techniques toautomatically form models of the surrounding built environment, usingthese models to evaluate different control strategies for determiningoptimal HVAC operating plans. As this technology is targeted towardsboth new and existing building stock and requires minimal capitalexpenditure, significant inroads can be made towards reducing operatingcosts with relatively short payback periods. Further, improvements inbuilding energy efficiency and performance ratings can be facilitatedthrough reduced energy consumption and associated CO₂ emissionreductions.

Assessing Thermal Comfort and Productivity

Although temperature most readily comes to mind when considering thermalcomfort, there are many other contributing factors. These include airvelocity, radiant temperature, humidity, metabolic rate and clothinglevel. The ASHRAE-55 (ASHRAE, 2004) standard for “Thermal EnvironmentalConditions for Human Occupancy”, details methods for theoreticallydetermining Predicted Mean Vote (PMV) and Predicted Percentage ofDissatisfied (PPD) occupants for a given set of conditions.

In assessing and predicting thermal comfort, the PPD metrics(implemented via the user interface of FIG. 5) are integrating with anoccupant comfort feedback application. In the case of the ASHRAEadaptive comfort standard, a wider range of conditions have been foundto be acceptable where a building is naturally ventilated and users havedirect control over their environmental conditions—such as byopening/closing windows. Similarly providing a mechanism for individualoccupant comfort feedback improves thermal satisfaction not only fromthe direct physical effect of user adjustments on indoor climate, butalso from empowerment of the occupants [Brager et al. 2004].

The occupant application can reside on an occupant's personal computer,informing them of a change in HVAC mode of operation (e.g. AirConditioning, Natural Ventilation, Peak Demand) via a small colour codedicon and informative “pop-up” message alerts. The above discussion dealswith assessing thermal comfort, however in the context of a workplacethere is the additional complicating question of what effect thermalcomfort has on productivity. Despite many studies attempting to quantifythis, results are far from clear and on assessing results from multiplestudies, Seppänen et al. (2003, 2006) found no statistically significantdifference in productivity for temperatures between 21 to 25° C. Withtemperatures above 25° C., Seppänen found a drop in productivity ofapproximately 2% per degree centigrade.

It was found that, while maintaining identical thermal comfort to theexisting BMS, substantial savings on both energy costs & CO₂ emissionsare feasible.

By allowing the building manager or user to determine the relativeweightings given to the competing performance objectives, they areempowered with explicit knowledge of tradeoffs being made when selectinga particular control strategy.

Example of a Building Model

This learning process model involves estimation of parameters of a modelthat aims to capture how the building responds to ambient temperature,as well as HVAC cooling and heating power. The parameter estimation is aleast-squared-error fit to a set of learning data. The learning data iscollected from a BMS either in real-time or off-line, from a BMS historyof set point values. The learning process is not affected by how thedata is collected (real-time or off-line), but it does require asufficient amount of data to be collected to ensure a “good enough” fit.

One embodiment of the model has the following form:

$\begin{matrix}{{T_{int}(z)} = {{{F_{amb}(z)}{T_{amb}(z)}} - {\frac{10}{P_{coolTyp}}{F_{Pcool}(z)}{P_{cool}(z)}} + {\frac{1}{P_{heatTyp}}{F_{Pheat}(z)}{P_{heat}(z)}} + {B(z)}}} & (1)\end{matrix}$

where: T_(int)(z) is the average internal building temperature;T_(amb)(z) is the ambient temperature; P_(cool)(z) is the HVAC coolingpower consumption; P_(coolTyp) is the typical HVAC cooling powerconsumption; it is used in Equation (1) as a scaling factor to get themagnitude of the parameters of F_(Pcool)(z) in a similar numerical rangeas other parameters; also it provides a normalization mechanism thatallows for operation on different BMS systems—this is particularlyimportant with respect to optimization constraints; P_(heat)(z) is theHVAC heating power consumption; P_(heatTyp) is the typical HVAC heatingpower consumption; it is used in Equation (1) as a scaling factor to getthe magnitude of the parameters of F_(Pheat)(z) in a similar numericalrange as other parameters; also it provides a normalization mechanismthat allows for operation on different BMS systems—this is particularlyimportant with respect to optimization constraints; F_(amb)(z)represents the internal building temperature response to ambienttemperature; F_(Pcool)(z) represents the internal building temperatureresponse to HVAC cooling power; F_(Pheat)(z) represents the internalbuilding temperature response to HVAC heating power; B(z), “baseline”,represents factors other than those represented by F_(amb)(z),F_(Pcool)(z); and F_(Pheat)(z); 10 is an arbitrary scaling factor usedto obtain the magnitude of the parameters of F_(Pcool)(z) in a similarnumerical range as other parameters; in other embodiments differentscaling factors are used.

In the above described model, the items of particular interest are thetransfer functions that express the dynamic response to ambienttemperature and heating/cooling power and the baseline. These transferfunctions are, in one embodiment, collections of 1^(st) order low-passfilters with different time constants, with each filter having the form:

$\begin{matrix}{{F(z)} = \frac{a}{z - \left( {1 - a} \right)}} & (2)\end{matrix}$

where z⁻¹ is the difference operator and a is given by:

$\begin{matrix}{a = \frac{h}{\tau - h}} & (3)\end{matrix}$

where τ is the system time constant and h is the sampling interval. Inother embodiments the transfer functions are indicative of other typesof functions such as higher order filter functions. As a rule of thumbit is necessary to ensure that the sampling is sufficiently fastcompared to the time constant, typically:

h≦τ/5  (4)

This is an important consideration when retrieving historical data froma BMS. In the discrete time domain, the first order filter of Equation(2) takes the form:

y(t _(k))=(1−a)y(t _(k-1))+ax(t _(k))  (5)

where x(t_(k)) is the input and is represented as per Equation (3) aboveand t_(k) is the sampling time of sample k. It should be noted that thepresently described embodiment uses x(t_(k-1)) instead of x(t_(k))—thisis a minimal difference and there should ideally be little if any effectin practice. In other embodiments, different representations ofx(t_(k-1)) are implemented. However, for the presently describedembodiment the following form will be used:

y(t _(k))=(1−a)y(t _(k-1))+ax(t _(k-1))  (6)

The notation can be simplified by using sample numbers only:

y(k)=(1−a)y(k−1)+ax(k−1)  (7)

Response to Ambient Temperature and HVAC Power

In the present embodiment, the building response to ambient temperatureas well as cooling/heating HVAC power is modeled as a set of three1^(st) order systems, each of the form of Equation (5), with differenttime constants. Specifically,

a _(1/h)=5/60,a=5/120,a _(5/h)=5/300  (8)

are the parameters of Equation (3) corresponding to time constants of1h, 2h and 5h time constants of three 1^(st) order responses (notingthat they are not quite in line with Equation (3) but close enough forpresent purposes. Given this, and with F_(1h), F_(2h), F_(5h) being the1^(st) order filters of the form of Equation (2) corresponding to thesetime constants, the dynamic responses to ambient temperature, HVACcooling power and HVAC heating power are modeled as:

F _(amb)(z)=p ₁₁ +p ₁₂ F _(1h)(z)+p ₁₃ F _(2h)(z)+p ₁₄ F _(5h)(z)  (9)

F _(Pheat)(z)=p ₂₁ +p ₂₂ F _(1h)(z)+p ₂₃ F _(2h)(z)+p ₂₄ F_(5h)(z)  (10)

F _(Pcool)(z)=p ₃₁ +p ₃₂ F _(1h)(z)+p ₃₃ F _(2h)(z)+p ₃₄ F_(5h)(z)  (11)

In the time domain, the dynamic response (or filtered response—hence thesuperscript F) to the above becomes:

T _(amb) ^(F)(k)=p ₁₁ +p ₁₂ T _(amb-1h)(k)+p ₁₃ T _(amb-2h)(k)+p ₁₄ T_(amb-5h)(k)  (12)

P _(heat) ^(F)(k)=p ₂₁ +p ₂₂ P _(heat-1h)(k)+p ₂₃ P _(heat-2h)(k)+p ₂₄ P_(heat-5h)(k)  (13)

P _(cool) ^(F)(k)=p ₃₁ +p ₃₂ P _(cool-1h)(k)+p ₃₃ P _(cool-2h)(k)+p ₃₄ P_(cool-5h)(k)  (14)

where:

T _(amb-Nh)(k)=(1−a _(Nh))T _(amb-Nh)(k−1)+a _(Nh) T _(amb)(k−1)  (15)

P _(cool-Nh) _(_)(k)=(1−a _(Nh))P _(cool-Nh)(k−1)+a _(Nh) P_(cool)(k−1)  (16)

P _(heat-Nh) _(_)(k)=(1−a _(Nh))P _(heat-Nh)(k−1)+a _(Nh) P_(heat)(k−1)  (17)

with N being 1, 2 and 5 for the 1h, 2h and 5h time constantsrespectively. The parameters p_(ij) express the relative contributionsof the dynamic responses corresponding to the various time constants.These parameters are estimated (“learned”) as described below in“Learning: Model Parameter Estimation”.

Applying the above equations to the overall building model of Equation(1) gives the following time domain version:

$\begin{matrix}{{T_{int}(k)} = {{T_{amb}^{F}(k)} - {\frac{10}{P_{coolTyp}}{P_{cool}^{F}(k)}} + {\frac{1}{P_{heatTyp}}{P_{heat}^{F}(k)}} + {B_{state}(k)}}} & (18)\end{matrix}$

Here the baseline B_(state)(k) is a catch-all function that captureschanges to the average internal temperature response outside what ismodeled by the ambient temperature and cooling/heating power response.The subscript “state” is either “week day” or “weekend”, with the formersignifying active building operation during typical working hours andthe latter signifying weekend operation. Thus, in effect there are twodifferent models depending on the day of the week.

In one embodiment the specific form of the baseline function is asfollows:

B _(state)(k)=Σ_(i=1) ¹¹ B _(h) _(i) (t _(k))  (19)

where B_(h) _(i) (t_(k)) represents a basis function and is given by:

$\begin{matrix}{{B_{h_{i}}\left( t_{k} \right)} = \left\{ \begin{matrix}\begin{matrix}{{\frac{B_{h_{i + 1}}}{h_{i + 1} - h_{i}}\left( {t_{k} - h_{i}} \right)} +} \\{\frac{B_{h_{i}}}{h_{i + 1} - h_{i}}\left( {h_{i + 1} - t_{k}} \right)}\end{matrix} & {{{if}\mspace{14mu} h_{i}} \leq t_{k} < h_{i}} \\0 & {otherwise}\end{matrix} \right.} & (20)\end{matrix}$

In Equation (20) the values B_(h) _(i) are estimated at specific,a-priori fixed points throughout the day h_(i). One form of theestimation process is described below. Equation (19) in practice equatesto sampling of a set of linear combinations of triangular shapedfunctions, as shown in FIG. 10. This figure illustrates establishing thevalue of B_(h) _(i) (t_(k)) at time t_(k), which falls betweenh_(i)≦t_(k)<h_(i+1). In line with Equation (19), the value of B_(h) _(i)(t_(k)) is a combination of the triangular function with the peak atB_(h) _(i) , and the triangular function with the peak at B_(h) _(i+1) .Based on this, the B_(state)(k) of Equation (19) is given by B_(h) _(i)(t_(k)) as all other triangular functions (a total of 12 inclusive ofB_(h) _(i) , B_(h) _(i−1) and B_(h) _(i+1) ) contribute 0.

The number 12 reflects the fact that there is expected to be asignificant difference in the baseline behaviour on a bi-hourly basis(captured by a peak of one of the triangular functions), with thein-between times adequately modelled by the linear combination of thetriangular functions, equivalent to linear interpolation between thepeaks of the contributing triangular functions.

FIG. 11 illustrates a full set of 12 hypothetical triangular functions,and the resulting B_(state)(k) (shown as the dotted envelope) for allt_(k). The peak values B_(h) _(i) are determined as part of the learningprocess discussed later.

The intent of the baseline function is to capture how the building load(outside what is captured by Equations (9) to (17)) varies throughoutthe day. For example, it is natural to expect that the influx of peoplein the early morning hours will have an effect on the building's thermaldynamics, as will the exodus of people during lunch hours, as well aslate during the day. There is a set of 12 triangular functions for theweek day baseline, and a separate 12 for the weekend baseline.

It will be appreciated that in other embodiments different forms ofbaseline functions can be implemented using different combinations ofbasis functions.

Learning: Model Parameter Estimation

The “learning” process of one embodiment consists of estimating theparameters p_(ij) in Equations (9) to (11), as well as B_(h) _(i) inEquation (20). In one embodiment the estimation process is a constrainedlinear least squares fit:

$\begin{matrix}{\hat{p} = {{\min\limits_{p}{{{{Dp} - T_{int}^{A}}}^{2}\mspace{14mu} {subject}\mspace{14mu} {to}\mspace{14mu} {Ap}}} \leq b}} & (21)\end{matrix}$

Where {circumflex over (p)} is a vector of estimated buildingparameters; D is a data matrix consisting of the filtered building dataas well as baseline function “values” (more below), p ranges over thebuilding parameter space with the constraint Ap≦b (more on theconstraint below). In explicit terms, Dp−T_(int) ^(A) has the form:

$\begin{matrix}{{{\begin{bmatrix}{T_{amb}^{FA}(0)} & {T_{heat}^{FA}(0)} & {T_{cool}^{FA}(0)} & {B(0)} \\\vdots & \vdots & \vdots & \vdots \\{T_{amb}^{FA}(k)} & {T_{heat}^{FA}(k)} & {T_{cool}^{FA}(k)} & {B(k)} \\\vdots & \vdots & \vdots & \vdots \\{T_{amb}^{FA}(K)} & {T_{heat}^{FA}(K)} & {T_{cool}^{FA}(K)} & {B(K)}\end{bmatrix}\begin{bmatrix}p_{11} \\p_{12} \\\vdots \\p_{34} \\B_{h_{1}} \\\vdots \\B_{h_{I}}\end{bmatrix}} - \begin{bmatrix}{T_{int}^{A}(0)} \\\vdots \\{T_{int}^{A}(k)} \\\vdots \\{T_{int}^{A}(K)}\end{bmatrix}}{{where}\text{:}}} & (22) \\{{T_{amb}^{FA}(k)} = \begin{bmatrix}1 & {T_{{amb} - {1h}}(k)} & {T_{{amb} - {2h}}(k)} & {T_{{amb} - {5h}}(k)}\end{bmatrix}} & (23) \\{{T_{cool}^{FA}(k)} = {\frac{- 10}{P_{coolTyp}}\begin{bmatrix}1 & {P_{{cool} - {1h}}(k)} & {P_{{cool} - {2h}}(k)} & {P_{{cool} - {5h}}(k)}\end{bmatrix}}} & (24) \\{{T_{heat}^{FA}(k)} = {\frac{1}{P_{heatTyp}}\begin{bmatrix}1 & {P_{{heat} - {1h}}(k)} & {P_{{heat} - {2h}}(k)} & {P_{{heat} - {5h}}(k)}\end{bmatrix}}} & (25)\end{matrix}$

In Equations (23) to (25), the row vector components T_(amb-Nh)(k),P_(cool-Nh)(k) and Pheat-Nh(k) are calculated as per Equations (9) to(11), with the T_(amb) _(_)(k−1), P_(cool) _(_)(k−1) and P_(heat)_(_)(k−1) being the actual ambient temperature, cooling power andheating power readings collected from the BMS at time t_(k); theabbreviation FA in T_(amb) ^(FA)(k), T_(cool) ^(FA)(k) and T_(heat)^(FA)(k) represents “filtered actual”, a reminder of the fact that therow vectors contain filtered versions of actual BMS data. The A inT_(int) ^(A)(k) also signifies actual BMS data—in the presentlydescribed embodiment it is the actual average internal buildingtemperature.

The final aspect of Equation (22) that has not been discussed so far isthe baseline values B(k). These are samples of the triangular functionscentered at h_(i) (as used in Equation (20)) with peaks at 1:

$\begin{matrix}{{\Delta_{h_{i}}(k)} = \left\{ \begin{matrix}0 & {{{if}\mspace{14mu} t_{k}} < {h_{i - 1}\mspace{14mu} {or}\mspace{14mu} t_{k}} \geq h_{i + 1}} \\\left( \frac{t_{k} - h_{i - 1}}{h_{i} - h_{i - 1}} \right) & {{{if}\mspace{14mu} h_{i - 1}} \leq t_{k} < h_{i}} \\\left( \frac{h_{i + 1} - t_{k}}{h_{i + 1} - h_{i}} \right) & {{{if}\mspace{14mu} h_{i}} \leq t_{k} < h_{i + 1}}\end{matrix} \right.} & (26)\end{matrix}$

The baseline values B(k) of the presently described embodiment are givenby samples of the triangular functions Δ_(h) _(i) (k):

B(k)=[B _(weekday)(k)B _(weekend)(k)]  (27)

B _(weekday)(k)=[Δ_(h) ₁ (k) . . . Δ_(h) _(i) (k) . . . Δ_(h) ₁₂ (k)0 00 0 0 0 0 0 0 0 0 0]  (28)

B _(weekend)(k)=[0 0 0 0 0 0 0 0 0 0 0 0Δ_(h) ₁ (k) . . . Δ_(h) _(i) (k). . . Δ_(h) ₁₂ (k)]  (29)

The above baseline values are scaled by appropriate choice of parametersB_(h) _(i) as determined through the constrained linear least squaresfit in Equations (21). In other embodiments, other baseline values B(k)and parameters B_(h) _(i) are implemented.

Returning to the constraints part of Equation (21), the matrix A isdesigned to achieve a number of constraint relationships:

-   -   The parameters p_(ij) and B_(h) _(i) must be positive.    -   The sum of the p_(ij)'s for ambient temperature filter T_(amb)        ^(F)(k) should be close to one; the intuitive meaning of this is        that the steady state of the ambient temperature filter should        be close to the actual ambient temperature.    -   However, provisions for this do exist within the model of the        preferred embodiment, with a constraint range of 2.0 and 4.0. In        other embodiments, the heating filter is employed.    -   The sum of the p_(ij)'s for cooling power filter P_(cool)        ^(F)(k) should be close to one; the intuitive meaning of this is        that the steady state of the cooling power filter should be        close to the actual cooling power temperature.    -   The baseline peaks should typically not exceed 20° C.

The specific form of A that achieves these requirements is:

$\begin{matrix}{A = \begin{bmatrix}{- I_{36 \times 36}} & \; & \; & \; \\I_{4 \times 1} & 0_{4 \times 1} & 0_{4 \times 1} & 0_{24 \times 1} \\{- I_{4 \times 1}} & 0_{4 \times 1} & 0_{4 \times 1} & 0_{24 \times 1} \\0_{4 \times 1} & I_{4 \times 1} & 0_{4 \times 1} & 0_{24 \times 1} \\0_{4 \times 1} & {- I_{4 \times 1}} & 0_{4 \times 1} & 0_{24 \times 1} \\0_{4 \times 1} & 0_{4 \times 1} & I_{4 \times 1} & 0_{24 \times 1} \\0_{4 \times 1} & 0_{4 \times 1} & {- I_{4 \times 1}} & 0_{24 \times 1} \\\; & 0_{12 \times 24} & I_{24 \times 24} & \;\end{bmatrix}} & (30)\end{matrix}$

where I_(m×m) is an identity matrix of size m×m and 0_(m×n) is a zeromatrix with m columns and n rows. The parameter estimation constraintsare contained in the vector b, with a specific example of this vectorgiven by:

$\begin{matrix}{b = \begin{bmatrix}0_{1 \times 36} \\1.5 \\{- 0.2} \\2.0 \\4.0 \\{- 0.2} \\2.0 \\20_{1 \times 24}\end{bmatrix}} & (31)\end{matrix}$

where in the above 20_(1×24) represents a vector of 24 values of 20.

Optimization

From a model estimated in accordance with the above described parametersit is possible to find optimal power profiles that meet certain ‘cost’targets and/or constraints. The discussion in this section is restrictedto the cooling case only. However, it will be appreciated that a similaroptimisation process is possible with models incorporating heating.

Consider, for example, a weather forecast given by T_(amb)={T_(amb)(1),. . . , T_(amb)(k)}. Consider also that a cooling power profile for thebuilding is chosen, which is given by P_(cool)={P_(cool)(1), . . . ,P_(cool)(k)}. It is possible to feed these two time series into filterequations (12) to (17) to obtain filtered versions, from which it ispossible to obtain the internal building temperature via Equation (18):T_(int)={T_(int)(1), . . . , T_(int)(k)}.

Having P_(cool) and T_(int) provides for assessing whether the chosenpower profile P_(cool) performs well or not. Specifically, one can lookat the cost of energy consumption and CO₂ emissions (based on P_(cool)),as well as the impact on occupant comfort (based on T_(int)).

The dollar cost of energy consumption of this embodiment is given by thefollowing:

$\begin{matrix}{C_{\$} = {\sum\limits_{i = 1}^{L}\; {{{Tariff}\left( t_{k} \right)}*{P_{cool}(k)}}}} & (32)\end{matrix}$

where Tariff(t_(k)) represents the energy tariff at the timecorresponding to sample k.

The cost of CO₂ emissions is given by:

$\begin{matrix}{C_{{CO}_{2}} = {\sum\limits_{i = 1}^{K}\; {P_{cool}(k)}}} & (33)\end{matrix}$

It is also possible to impose a cost on deviations from a predeterminedtarget average comfort level, as follows:

$\begin{matrix}{{C_{comf}\left( {PPD}_{target} \right)} = {\sum\limits_{i = 1}^{K}\; {{{{PPD}\left( {T_{int}(k)} \right)} - {PPD}_{target}}}^{2}}} & (34)\end{matrix}$

We can combine these three cost components into a single cost function:

C(P _(cool) |T _(amb))=w ₁ C _($) +w ₂ C _(CO) ₂ +C _(comf)(PPD_(target))  (35)

In Equation (35), the three parameters w₁, w₂ and PPD_(target) are userconfigurable. The P_(cool) parameter in C(P_(cool)|T_(amb)) is there toemphasize that, for a given ambient temperature forecast, the entirecost function depends only on the chosen power profile.

The cost function allows one to find an optimal power profile usingstandard optimization. Of course, alternative or modified cost functionscan also be utilised.

Alternative Model Including Heating

One form of extension of the previous models to also include heatingoptimizations will now be described. The extension allows for additionalbuilding operation types, heating and fuel source mixes, and inalternative optimisation and modelling methods. The models can beextended to allow for the identification of the effect of heat energy,electric and non-electric fuel sources, and mixed heating and coolingsituations on the energy consumption, comfort levels and CO2 emissionsof a building.

The alternative model has been designed for testing against a buildinghaving a conventional gas boiler heating system, hot and chilled waterloops and VAVs. Of course, customization to any particular buildingshould also be carried out. The example building for which the model wasdeveloped was located in Victoria, Australia and had the followingcharacteristics: Construction: Blockwork, built 2006; Floor area: 1808m2, 3 levels, offices, Operation: Mixed mode—natural ventilation withfans, automatic windows, Heating: Raypak 868 gas boiler—868 kWth (link),Cooling: York YCA 0235 6-stage Air-Cooled Scroll Chiller—235 kWthnominal (link); BMS: Siemens Desigo v3.0, Siemens BACNet Server;Metering: Gas volume meter, electrical submetering—mechanical services &whole building.

This alternative model provides for extending the structure of thebuilding energy model to allow learning of the effect of both heatingand cooling on zone temperature. The model also allows for optimizationof the consumption of both heating and cooling energy. The model alsodeals with non-electric fuel sources. This includes consideration ofcapacity, pricing structures and greenhouse gas emissions. The modelalso allows for dealing with multiple, possibly simultaneous, energysources.

The previous cooling only models were designed towards buildingsoperating in warm climates where HVAC energy consumption is dominated bycooling. While cooling is almost exclusively achieved using electricchillers, there are a number of different systems and fuel typescommonly used to deliver heating. Additionally, multiple differentsystems may be installed and even run simultaneously on singlebuilding—significantly complicating the implementation.

Although buildings may have multiple heating/cooling systems, withsubstantial flexibility in determining which to use under givenconditions, the approach used with this alternative model is to allowthe existing BMS to determine the appropriate combination of plant touse to affect a given conditioning setpoint. At a high level, thisalternative model learns the relationship between energy greenhousegases and building conditions and applies optimised zone conditionsetpoints. At a low level, this alternative model can be used to lockout or use certain plant preferentially, though this is not part of thecore optimisation. When low level changes are enacted, this alternativemodel sees these through changes in condition/energy relationships andupdates the building model accordingly.

Zone Level Heating/Cooling Control

The initially discussed model, used a zone level PMV setpoint at the keycontrol variable. For this cooling dominated case, heating was carriedout using a rule based approach (heat to a minimum acceptable comfortlevel and no further), and the PMV setpoint was interpreted as thetargeted level of cooling. The individual zone control algorithm wasessentially: If T_(Zone)<T_(Min) _(_) _(Allowed) then Heat_To_T_(Min)else Cool_To_PMV_Setpoint end

Exactly how these heating/cooling setpoints were realised, was thendependant on the specific BMS and building configuration—includingcontrol of supply air setpoints, chilled & hot water valves, etc. It isimportant that this low level BMS interface ensures that energy is notwasted cooling below the cooling setpoint, or heating above the heatingsetpoint (for example having electric reheats come on when zone setpointis raised with the intent of reducing cooling power). In order to allowboth heating and cooling to be optimised, while minimising thepossibility of simultaneous heating/cooling (which for adjacent zonescan be very energy wasteful), the high level building optimisation ofthe alternative model is modified to produce two setpoints—a coolingsetpoint PMV and a heating setpoint PMV. The basic individual zonecontrol algorithm is then modified to essentially implement: IfPMV_(Zone)<PMV_(Heat) _(_) _(Setpoint) then Heat_To_PMV_(Heat) _(_)_(Setpoint) else Cool_To_PMV_(Cool) _(_) _(Setpoint) end which isessentially the same as previously, however both heating and coolingsetpoints are both expressed in PMV and vary dynamically per theoptimisation. This requires minimal changes to the low level zonecontroller.

To facilitate the inclusion of heating, cooling and different fuelsources, the structure of the ‘grey box’ building model was revised. Anupdated formulation was as follows:

T _(z) =F _(A)(s)·T _(Amb)+BaselineFcn−F _(T)(s)·ΔT _(SS)

where: {circumflex over (T)}_(z) is (modelled) aggregate zonetemperature; T_(Amb) is the outside (Ambient) air temperature; ΔT_(SS)is the steady state difference in zone temperature that would resultfrom the current HVAC cooling and heating powers; BaselineFcn is alearnt function of time, accounting for people, equipment, sun, etc;F_(A)(s) and F_(T)(s) are linear time invariant filters, accounting forthe system dynamics. Furthermore, we denote:

T _(ZF) =F _(A)(s)·T _(Amb)+BaselineFcn

as the (modelled) free-running zone temperature—that is, our estimate ofwhat the aggregate building zone temperature would have been without theHVAC system running; and

ΔT _(Z) =F _(T)(s)·ΔT _(SS)

as the difference in zone temperature due to the HVAC system.

The filters F(s), were, and remain 3^(rd) order LTI with feed-throughand time constants at 1, 2 and 5 hours. Specifically:

${{F_{T}(s)} = {k_{{T\_}0} + \frac{k_{{T\_}1}}{{\tau_{1} \cdot s} + 1} + \frac{k_{{T\_}2}}{{\tau_{2} \cdot s} + 1} + \frac{k_{{T\_}3}}{{\tau_{5} \cdot s} + 1}}};$and${{F_{A}(s)} = {k_{{A\_}0} + \frac{k_{{A\_}1}}{{\tau_{1} \cdot s} + 1} + \frac{k_{{A\_}2}}{{\tau_{2} \cdot s} + 1} + \frac{k_{{A\_}3}}{{\tau_{5} \cdot s} + 1}}};$

where k_(T) _(_) ₀, k_(T) _(_) ₁, k_(T) _(_) ₂, k_(T) _(_) ₃, k_(A) _(_)₀, k_(A) _(_) ₁, k_(A) _(_) ₂ & k_(A) _(_) ₃ are filter gains that areidentified, and τ₁, Σ₂ & τ₅ are the 1, 2 & 5 hour time constantsrespectively.

The BaselineFcn is represented by two vectors, BaselineWeekday andBaseline Weekend, each of dimension 1×12 which are interpreted as theoffset temperatures (in ° C.) that are added to the modelled averagezone temperature at times [0 2 4 8 10 12 14 16 18 20 22] hours into the(week or weekend) day. When calculating the appropriate BaselineFcnvalue at other times, a linearly interpolation can be undertaken betweenthe two nearest values. One difference in the alternative model is thatthe normalised HVAC cooling power has now been replaced withΔT_(SS)—which represents the aggregate impact of multipleheating/cooling sources on the zone temperatures.

Heating/Cooling Power Relationships

While the previous models were aimed at cooling dominated scenarios, inorder to handle the heating case, an alternative power model structureis desired. Core factors include: where diversity between zones meanthat although the aggregate zone temperature might be at setpoint, bothheating and cooling energy need to be used to maintain individual zonesat a setpoint; rather than treating cooling and heating as beingproportional to the applied HVAC power, it needs to be acknowledged thatthere are likely a number of reasonably fixed loads (ie fans & pumps)associated with the HVAC system running even before any notablecooling/heating is achieved. Some of this baseline may also be due toother site loads. Another factor is that efficiency of heating/coolingsystems changing with ambient temperature—a specific example being thedecrease in COP (coefficient of performance) of chillers with increasingambient temperature. Increased use of external air in preference torunning chillers/heaters (day-purge) also has this impact.

The following relationship between measured power and impact onaggregate zone temperature were utilised:

ΔT _(SS)=α_(c)·μ_(c)·max{0,P _(Cool) −P _(cb)}−α_(h)·μ_(h)˜max{0,P_(Heat) −P _(hb)}

where the first part of the equation is the effective coolingtemperature (ΔT_(Cool)), the second part is the effective heatingtemperature (ΔT_(Heat)), and the parameters are: P_(Cool) and P_(Heat)are actual cooling and heating powers respectively (kW); P_(cb) andP_(hb) are baseline cooling and heating powers respectively (kW); α_(c)and α_(h) are nominal scaling for HVAC power effectiveness (° C./kW);and μ_(c), and μ_(h) are HVAC efficiency de-ratings as a function ofexternal temperature.

The de-ratings are parameterised as:

μ_(c)=min{1,1+α_(cd) [T _(cx) −T _(Amb)]};

and

μ_(h)=min{1,1−α_(hd) [T _(hx) −T _(Amb)]}.

T_(cx) is the temperature above which cooling de-rating occurs, whileT_(hx) is the temperature below which heating de-rating occurs. Typicalvalues might be 20° C. α_(cd) and α_(hd) are the de-ratingfractions—typically around 0.02/° C.

Additionally, to emulate mixed heating/cooling scenarios, effectivecooling is considered to occur for ΔT_(SS)>ΔT_(c0) and heating forΔT_(SS)<ΔT_(h0). Typical values of these would be ΔT_(c0)=−0.5° C. andΔT_(h0)=0.5° C. —meaning that for ΔT_(SS) between −0.5 to 0.5° C., therewould be a combination of both heating and cooling occurring.

FIG. 12 illustrates the interrelationship of these variables. Thecombined heating and cooling power now gives total building power thatcan match the ‘V’ or parabolic type relationship that we expect forbuilding power as a function of external temperature.

Fitting to the Revised Building Model

In the revised model, fitting of the building model is performed onceper day, as the system is restarted. Data from a building log file isread, and time series data is extracted for the signals: This data caninclude: T_(z)—the aggregate zone temperature, taken as a weightedaverage of all zone temperatures—based on a ‘Config_ZoneSizes’configuration parameter; P_(Cool)—taken as a sum of all cooling relatedpower measurements, as described below; P_(Heat)—taken as a sum of allheating related power measurements, as described below; and T_(Amb)—themeasured ambient (outside) temperature.

Ideally these data sets should comprise 2-3 months continuous data.Where this is not the case, small data gaps can be interpolated over.Where there are large gaps in the data, the data can be broken intomultiple sets and once the data is filtered the first 5 hours of eachset is discarded to minimise the impact of unknown initial conditions.

The assessment of model fit is based on 2-norm—that is, model parametersare chosen within allowable ranges to minimise ∫(T_(z)-T _(z))² dt, thesquared error between the modelled and measured aggregate building zonetemperature.

The model fit can be programmed as a nested optimisation:

${\min\limits_{PowerParamaters}{{{T_{z} - {\overset{\sim}{T}}_{z}}}_{2}\mspace{14mu} {where}}}\;$$\mspace{11mu} {{\overset{\sim}{T}}_{z}\text{:}\mspace{14mu} \left\{ {{\min\limits_{FilterParameters}{{T_{z} - {\overset{\_}{T}}_{z}}}_{2}}_{PowerParameters}} \right\}}$

with PowerParameters are P_(cb), P_(hb), α_(c), α_(h), μ_(c), μ_(h),α_(cd) and α_(hd); FilterParameters are k_(T) _(_) ₀, k_(T) _(_) ₁,k_(T) _(_) ₂, k_(T) _(_) ₃, k_(A) _(_) ₁, k_(A) _(_) ₂, k_(A) _(_) ₃,BaselineWeekday and BaselineWeekend; and as a final step ΔT_(c0) andΔT_(h0) are fitted based on the learned model.

In implementing this model fit, the Matlab lsqlin function (leastsquares with linear constraints) can be used for fitting theFilterParameters, while fmincon (multidimensional constrained nonlinearminimisation) can be used for the PowerParameters search. The model wasbroken up this way to reduce the dimension of the required nonlinearminimisation—which is a harder problem than the linear case. The modelfitting routine has been updated so that rather than having limits ofthese parameter values hard coded into the routine, these are now passedin, as upper and lower bounds for each parameter. If a parameter is notto be fitted, these upper and lower bounds can be set equal.

Optimising Building Setpoints with the Revised Building Model

In the alternative model, the methodology for the building setpointoptimisation can be revised to take into account the heating case.Previously, the optimisation returned an optimised power profile for thebuilding, which was then used to determine appropriate PMV setpoints foreach zone while tracking this profile. In the alternative model, therevised optimisation explicitly provides dual heating and cooling targetPMV setpoints in addition to both expected heating and cooling powers.The PMV setpoints are now treated as the primary optimised setpoints,and are only relaxed if anticipated power usage is being exceeded. This,and a revised approach to initial conditions calculation, helps overcomesome of the sensitivity to fluctuations in the power measurements—unlessanticipated power usage is exceeded, the building will operate on PMVsetpoints.

The dual PMV setpoints are derived through a similar optimisationprocess as previously, however ΔT_(SS) is now the optimised variablerather than cooling power. From ΔT_(SS), anticipated heating/coolingpower is determined from the nonlinear maps, allowing calculation ofpower cost, greenhouse gas cost and PMV. From the optimised PMV, thedual PMV setpoints are given as

${PMV}_{Cool} = \left\{ {{\begin{matrix}{{PMV}_{Opt};} & {{\Delta \; T_{ss}} \geq {0\mspace{14mu} ({Cooling})}} \\{{PMV}_{{Cool}\_ {Min}};} & {otherwise}\end{matrix}{PMV}_{Heat}} = \left\{ \begin{matrix}{{PMV}_{Opt};} & {{\Delta \; T_{ss}} < {0\mspace{14mu} ({Heating})}} \\{{PMV}_{{Heat}\_ {Max}};} & {otherwise}\end{matrix} \right.} \right.$

that is, when the building is in aggregate heating, any zones that needcooling should only be cooled to the minimum acceptable PMV (noting PMVscale goes from −3:Cold to 3:Hot), while zones being heated shouldtarget the optimised PMV setpoint. Similar formulations can beimplemented for the cooling mode.

The setpoint optimisation runs each 5 minutes based on updatedinformation on: Actual Building Zone temperatures; Energy Prices; amdWeather forecasts. These are used in conjunction with the previouslydetermined building model, which gives the expected relationship betweenheating and cooling powers and building thermal condition:

T _(z) =F _(A)(s)·T _(Amb)+BaselineFcn−F _(T)(s)·ΔT _(SS)

The optimisation seeks to minimise:

J(ΔT _(SS))=W _(CO2) ·CO2+W _(Cost)·Cost; s.t. average PPD≦Av _(PPD)

where: CO2 is the estimated CO₂ impact of the proposed run schedule forthe remainder of the day; Cost is the estimated monetary costs of theproposed run schedule for the remainder of the day; average PPD is theestimated average PPD achieved for the whole of the day; W_(CO2) &W_(Cost) are (scalar) weights used to apportion the relative importanceof these metrics to the optimisation; and Av_(PPD) is the target maximumallowable average PPD for the building over the day.

In assessing this cost function, there is a static (nonlinear) map asdescribed in the previous section between ΔT_(SS) and heating/coolingpower—and hence energy & CO₂ costs. To assess the PMV and PPD profilefor the remainder of the day, an estimate of the future weatherconditions is required. From the BMS, we have a data history of T_(Amb),and from the BOM (plus any localised weather learning algorithm), wehave the forecast ambient temperature T_(Forecast). These two data setsmust be merged together so that there is not a discontinuity in thedata. This merge of historic and forecast ambient temperature occursover a 3 hour interval and the subsequent data set is denotedT_(Predicted). The merging process is illustrated in FIG. 13.

Dealing with Initial Conditions

The previous models relied upon measured cooling power and ambienttemperature to initialise model dynamics. This could cause problemswhere measured power was significantly different from the anticipatedmodelled power (for example due to compressor staging) or where thebuilding dynamics and loads (usage pattern) were significantly differentfrom those modelled. This can manifested itself as a discontinuitybetween measured behaviour (up to current time) and the forecastbehaviour moving forward. To help overcome this and remove as muchdependency on the power modelling, the optimization can use a state‘estimator’ (observer) to model the building dynamic state—and provide afree running response. This allows the optimisation routine to only needdeal with a zero-initial-condition case in calculating the buildingresponse to the proposed ΔT_(SS).

The estimated conditioning is obtained by rearranging the buildingmodel:

=F _(T) ⁻¹(s)[F _(A)(s)·T _(Amb)+BaselineFcn−T _(z)];

up until time t_(now), and the free-running building response (no HVAC)is obtained by setting

=0 for time greater than t_(now) and calculating:

=F _(A)(s)·T _(Amb)+BaselineFcn−F _(T)(s)·

and the controlled building zone temperature response is then given by:

=F _(A)(s)·T _(Amb)+BaselineFcn−F _(T)(s)·

−F _(T)(s)·ΔT _(SS)

where F_(T)(s)·ΔT_(SS) is the optimised zero initial condition responsefor time>t_(now) and the other filter dynamics have been allowed toevolve over the previous day data to have appropriate state at timet_(now).

Catering for Different Fuel Types

The alternative model is also able to deal with different fuel types.The main issues here are: Different fuel types have different greenhousegas potentials; different fuel types have different pricing structures;and different measurement methods are used to monitor fuel usage.

In Australia, the relative impacts of different energy sources arecalculated by the Australian Government—Department of Climate Change andEnergy Efficiency (DCCEE). Each year these figures are updated andpublished as the ‘National Greenhouse Accounts (NGA) Factors’ [1]. Thefactors change depending on different mining methods, fuel mixes,distribution losses etc and consequently vary over both time andgeographic location. In reporting greenhouse gas impacts, there are 3different types of emission factors used: Scope 1 Emissions—these arethe direct CO₂ equivalent emissions from an activity (for example, theCO₂ directly released in burning natural gas, ignoring what was involvedin extracting/refining/transporting the gas); Scope 2 Emissions—theseare the indirect CO₂ equivalent emissions from the generation ofelectricity, purchased and consumed by an organisation, to conduct anactivity (that is, the scope 1 emissions that a power station incurs onyour behalf in generating electricity for you); Scope 3 Emissions—theseare the various additional emissions associated with extraction,production, transport, generation, distribution/transmission etc of afuel. This includes electrical network losses. An assessment of the fullfuel cycle costs include Scope 3 emissions.

For the commercial building sector, the relative proportions ofdifferent fuel types used, as reported as used in Australian commercialbuildings are shown below in FIG. 14. This is (unsurprisingly) dominatedby the use of electricity and natural gas. Latest estimates (per July2010, from [1]) of the full fuel cycle of these fuels in Australia areset out in the following table (noting that IMWh=3.6 GJ):

Natural Gas (metro) Electricity kgCO₂-e/GJ kgCO₂-e/GJ (kgCO2-e/kWh) FullFull Scope 1 Scope 3 Cycle Scope 2 Scope 3 Cycle NSW 51.33 14.2 65.53249 (0.9) 48 (0.17) 298 (1.07) Vic 51.33 4.0 55.33 342 (1.23) 39 (0.14)382 (1.37) Qld 51.33 8.6 59.93 247 (0.89) 36 (0.13) 283 (1.02) SA 51.3310.4 61.73 200 (0.72) 37 (0.13) 236 (0.85) WA 51.33 4.0 55.33 228 (0.82)29 (0.1) 257 (0.93) (SWIS) Tas 51.33 NA NA  89 (0.32)  8 (0.03)  96(0.35) NT 51.33 NA NA 189 (0.68) 26 (0.09) 215 (0.77)

Configuration Changes to Cater for Different Fuel Types and MeasurementMethods

The previous models only effectively handle one type of powermeasurement—electrical kW, contributing to cooling. In the alternativemodel, this is updated by the inclusion of configuration parameters.

The alternative model includes 5 configuration variables:

Config_PowerWeights 1 0.72 278 Config_CarbonWeights 1.07 1.07 0.236Config_PowerTypes CP CP HE Config_PowerPrices 1 1 2Config_PowerPriceNames ‘Elec TOU’ ‘Gas’

Although many types of normalisation could be used, scaling factors needto provide a mechanism for comparing the relative effect of differentfuel and measurement types. The scaling factors have been nominallyconsidered to convert the measured quantities into kW (or kWh) forcomparing power, and kgCO₂-e/kWh for comparing greenhouse impact. ThePowerWeights configuration variable scales to kW (or kWh). TheCarbonWeights variables scales to kgCO₂-e. The PowerTypes variableclassifies each power measurement as either contributing to cooling (C)or heating (H), and then of measurement type power (P) or energy (E). Apower measurement is (for example) a direct kW measurement. An energymeasurement is through a cumulative register, ie kWh, and must bedifferentiated with respect to time to determine a power level. Validvalues for PowerTypes are ‘CP’, ‘CE’, ‘HP’ and ‘HE’. PowerPriceNamesholds the names of different energy pricing configurations. PowerPricesprovides an index into PowerPriceNames to determine which energy pricingstructure applies to each power measurement.

For the specific configuration values in the example above, there are 3measured power data points. These will be named Power_1, Power_2 andPower_3 in the building configuration file. Power_1 is measured directlyin kW, so PowerWeights=1. The scaling factor to CO₂-e is 1.07 (for NSW).This energy is used for cooling with power being directly measured ‘CP’.The energy pricing type is ‘Elec TOU’ hence index 1 intoPowerPriceNames. Power_2 is obtained by measuring amps on 1 phase of abalanced 3 phase system—hence PowerWeights is set to 0.72 since 1measured amp corresponds to 720 W power. Other scaling factors are sameas Power_1. Power 3 is gas for heating. It is measured using anaccumulation meter with units GJ. PowerWeights of 278 converts GJ toequivalent kWh. CarbonWeights of 0.236 is the kgCO₂-e that one kWhequivalent of natural gas consumption equates to. PowerPrices is 2,being the index into PowerPriceNames for the Gas price structure.

Although the names of the various power pricing structures are stored inthe configuration file, the actual configuration of the pricing levelsis done through the ‘Energy pricing Configuration’ GUI, which has beenupdated to allow for multiple fuel types (see EnergyPriceConfigV2.m).This allows a TOU pricing structure to be set for each fuel type—whichcan just be a fixed constant price, such as for gas. FIG. 15 illustratesand updated GUI for data entry. Units are nominally taken as c/kWh,though this is of course arbitrary.

REFERENCES

-   Australian Greenhouse Office (1999), Australian Commercial Building    Sector Greenhouse Gas Emissions 1990-2010. Available online at    http://www.environment.gov.au/[Accessed 17 Jun. 2008]-   Braun, J. E. (1990), Reducing Energy Costs and Peak Electrical    Demand Through Optimal Control of Building Thermal Storage, ASHRAE    Trans. Vol 96(2), pp. 876-888-   Braun, J. E., Montgomery, K. W. and Chaturvedi, N. (2001),    Evaluating the performance of building thermal mass control    strategies. HVAC&R Research. Vol 7(4) pp 403-428.-   Eto, J. (2007), Demand Response Spinning Reserve Demonstration.    Ernest Orlando Lawrence Berkeley National Laboratory. Berkeley    Calif., USA. http://eetd.lbl.gov/ea/EMS/EMS_ubs.html [Accessed 17    Jun. 2008]-   Fanger, P. O. (1967), Calculation of thermal comfort: introduction    of a basic comfort equation. ASHRAE Transactions 73(2):III.4.1.-   Seppänen, O., Fisk, W. J. and Lei, Q. H. (2006), Room temperature    and productivity in office work, Lawrence Berkeley National    Laboratory, University of California.    http://repositories.cdlib.org/lbnl/LBNL-60952 [Accessed 17 Jun.    2008]-   White, S. and Ward, J. K. (2006), Performance of a Microturbine    Power and Desiccant Cooling Demonstration. IIR-IRHACE International    Conference 2006. Auckland, New Zealand. 16th-18th Feb. 2006.-   Burress, C. (2008), State abandons plan to allow utilities to    control home thermostats, San Francisco Chronicle, Jan. 17, 2008.    [Online]. Available: http://www.sfgate.com [Accessed May 1, 2008].-   Australian Government Department of Climate Change (2008), National    Greenhouse Accounts (NGA) Factors. http://www.climatechange.gov.au    [Accessed 17 Jun. 2008]-   ASHRAE (2004), ANSI/ASHRAE Standard 55-2004, Thermal Environmental    Conditions for Human Occupancy. American Society of Heating,    Refrigerating and Air-Conditioning Engineers. Atlanta, USA.    www.ashrae.org-   Brager, G., Paliaga, G. and de Dear, R. J. (2004), Operable windows,    personal control and occupant comfort. ASHRAE Trans., Vol. 110(2),    pp. 17-35.-   Seppänen, O., Fisk, W. J. and Faulkner, D. (2003), Cost benefit    analysis of the night-time ventilative cooling. Proceedings of the    Healthy Buildings 2003 Conference. Singapore 2003, Vol 3 pp 394-399.-   National Greenhouse Accounts (NGA) Factors. Department of Climate    Change and Energy Efficiency, Commonwealth of Australia 2010. ISBN:    978-1-921299-04-9

INTERPRETATION

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure or characteristicdescribed in connection with the embodiment is included in at least oneembodiment of the present invention. Thus, appearances of the phrases“in one embodiment” or “in an embodiment” in various places throughoutthis specification are not necessarily all referring to the sameembodiment, but may. Furthermore, the particular features, structures orcharacteristics may be combined in any suitable manner, as would beapparent to one of ordinary skill in the art from this disclosure, inone or more embodiments.

Similarly it should be appreciated that in the above description ofexemplary embodiments of the invention, various features of theinvention are sometimes grouped together in a single embodiment, figure,or description thereof for the purpose of streamlining the disclosureand aiding in the understanding of one or more of the various inventiveaspects. This method of disclosure, however, is not to be interpreted asreflecting an intention that the claimed invention requires morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive aspects lie in less than allfeatures of a single foregoing disclosed embodiment. Thus, the claimsfollowing the Detailed Description are hereby expressly incorporatedinto this Detailed Description, with each claim standing on its own as aseparate embodiment of this invention.

Furthermore, while some embodiments described herein include some butnot other features included in other embodiments, combinations offeatures of different embodiments are meant to be within the scope ofthe invention, and form different embodiments, as would be understood bythose in the art. For example, in the following claims, any of theclaimed embodiments can be used in any combination.

Furthermore, some of the embodiments are described herein as a method orcombination of elements of a method that can be implemented by aprocessor of a computer system or by other means of carrying out thefunction. Thus, a processor with the necessary instructions for carryingout such a method or element of a method forms a means for carrying outthe method or element of a method. Furthermore, an element describedherein of an apparatus embodiment is an example of a means for carryingout the function performed by the element for the purpose of carryingout the invention.

In the description provided herein, numerous specific details are setforth. However, it is understood that embodiments of the invention maybe practiced without these specific details. In other instances,well-known methods, structures and techniques have not been shown indetail in order not to obscure an understanding of this description.

As used herein, unless otherwise specified the use of the ordinaladjectives “first”, “second”, “third”, etc., to describe a commonobject, merely indicate that different instances of like objects arebeing referred to, and are not intended to imply that the objects sodescribed must be in a given sequence, either temporally, spatially, inranking, or in any other manner.

In the claims below and the description herein, any one of the termscomprising, comprised of or which comprises is an open term that meansincluding at least the elements/features that follow, but not excludingothers. Thus, the term comprising, when used in the claims, should notbe interpreted as being limitative to the means or elements or stepslisted thereafter. For example, the scope of the expression a devicecomprising A and B should not be limited to devices consisting only ofelements A and B. Any one of the terms including or which includes orthat includes as used herein is also an open term that also meansincluding at least the elements/features that follow the term, but notexcluding others. Thus, including is synonymous with and meanscomprising.

Similarly, it is to be noticed that the term coupled, when used in theclaims, should not be interpreted as being limitative to directconnections only. The terms “coupled” and “connected,” along with theirderivatives, may be used. It should be understood that these terms arenot intended as synonyms for each other. Thus, the scope of theexpression a device A coupled to a device B should not be limited todevices or systems wherein an output of device A is directly connectedto an input of device B. It means that there exists a path between anoutput of A and an input of B which may be a path including otherdevices or means. “Coupled” may mean that two or more elements areeither in direct physical or electrical contact, or that two or moreelements are not in direct contact with each other but yet stillco-operate or interact with each other.

Although the present invention has been described with particularreference to certain preferred embodiments thereof, variations andmodifications of the present invention can be effected within the spiritand scope of the following claims.

1-13. (canceled)
 14. A method of controlling the heating, ventilationand air conditioning (HVAC) system of a building, the method comprisingthe steps of: (a) determining a thermal model for the building; (b)determining expected external meteorological conditions for an areasurrounding the building; (c) determining an external meteorologicalcondition model for the HVAC system; (d) utilising the externalmeteorological condition model as the prime factor in calculating anHVAC operating plan of the building.
 15. The method of claim 14, whereinsaid external meteorological condition model is augmented with data frommeteorological data suppliers.
 16. A method of controlling the heating,ventilation and air conditioning (HVAC) system of a building, the methodcomprising the steps of: (a) determining a thermal model for thebuilding; (b) determining an expected human comfort model for users ofthe building; (c) determining a power consumption or carbon emissionmodel for the HVAC system; (d) determining a energy cost model for theHVAC system; (e) determining an external meteorological condition modelfor the HVAC system; (f) applying relative weightings of two or more ofthe expected human comfort model, power consumption or carbon emissionmodel, energy cost model, and external meteorological condition modelfor the HVAC system in calculating an HVAC operating plan of thebuilding.
 17. The method of claim 16, wherein said human comfort modelis augmented with personal comfort data of users of the building bymeans of data feed back from users of the building.
 18. The method ofclaim 16, wherein said human comfort model is derived from the ASHRAEstandard comfort models.
 19. The method of claim 16, wherein said powerconsumption or carbon emission model and said energy cost model isaugmented with consumption and pricing data from energy suppliers. 20.(canceled)
 21. The method claim 14, wherein said thermal model isiteratively updated substantially daily.
 22. The method of claim 14,wherein said HVAC operating plan is recalculated substantially inincrements of minutes. 23-29. (canceled)